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Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

Antal A. Jarai·Frank Redig
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Abstract

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.

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BibTeXRIS

Antal A. Jarai, Frank Redig. 2004-08-04. Infinite volume limit of the Abelian sandpile model in dimensions d >= 3. https://doi.org/10.1007/s00440-007-0083-0

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